Common Student Math Misconceptions

Beware of Mistakes Ahead road sign

Students make math mistakes for many reasons.  They rush through their work or lose focus and make a copy error.  Sometimes that sneaky little minus sign just doesn’t make its way to the next line of algebra work.  But other times, mistakes happen even when students are thinking deeply about the concepts and concentrating on every detail that they write.  When this occurs, it is most likely because of a math misconception.

These math misconceptions are important for teachers to recognize: to identify why a student made a mistake and how to address it.  A seasoned teacher will have a pocketful of misconceptions that students are likely to make. The teacher will use this information to aid instruction, through teaching with multiple representations and encouraging student discourse in the classroom.

So, what are some examples of misconceptions?

Here are a couple:

One of the most prevalent mistakes in an algebra classroom is expanding (x+y)2 to equal x2+y2.  Students will often give a good reason for this: they just distribute the exponent to each term in the parentheses.  Why?  The distributive property states that 2(x+y)=2x+2y, so “of course” squaring behaves the same way as multiplication. Right? Wrong!!

The correct answer is actually x2+2xy+y2, which can be shown if students understand what “squaring” means.  Consider these representations:

 

22 

 

52

 

 

(x+y)2

x               y

     x2        

       xy        

 xy

      y2

 x

  y

 

Another misconception occurs when students develop a way to solve one problem that fails to generalize to all problems.  Consider the following table:

 

         x        

        y         

0

1

1

2

2

3

3

4

4

5

 

The rule: y=x+1 is correct for this data set, but a common misconception is that the rule is the same as the pattern.  A student may notice that since the y-values increase by 1, the rule for the pattern will be to “add one.”  But when this strategy is applied to the following data set, it fails.

 

     x       

    y       

0

2

1

3

2

4

3

5

4

6

 

Here the correct rule is y=x+2.  

Why?  

The rule tells us how to go from x to y, not how the y-values grow.  Having students discuss their methods or communicate explanations clearly can allow these misconceptions to come to light.  It’s also important that examples where this can happen are avoided.

When teachers understand common misperceptions that students hold of the material under study, they can structure their lessons to enable students to uncover and eliminate these misconceptions.  Of course, teachers are not the only educators who benefit from understanding common misperceptions.  Content developers need to use this same understanding to craft resources that enable a consideration of misconceptions.  Test writers need to use this same understanding to create plausible distractors for selected response items.

By | 2018-07-22T17:55:58+00:00 May 11th, 2016|classroom teaching, math, Teaching|0 Comments

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